Entrained Bed Entrained Bed ReactorReactor

Quak Foo LeeQuak Foo Lee

Department of Chemical and Biological Department of Chemical and Biological EngineeringEngineering

Entrained Bed ReactorEntrained Bed Reactor Entrained bed, pneumatic transport reactorEntrained bed, pneumatic transport reactor

Riser reactor, raining bed reactorRiser reactor, raining bed reactor Dilute suspension of solids and usually Dilute suspension of solids and usually

reactors have large L/D ratioreactors have large L/D ratio Near plug flowNear plug flow If feed particles are all of the same size, them If feed particles are all of the same size, them

all have same residence timeall have same residence time

Entrained Bed ReactorEntrained Bed Reactor Advantage is one can control the Advantage is one can control the

residence timeresidence time

Small particle and co-current flowSmall particle and co-current flow

Simplified analysisSimplified analysis Flat velocity profile for gasFlat velocity profile for gas Plug flow of solidsPlug flow of solids Isothermal Isothermal Constant fluid propertiesConstant fluid properties

Reactor ConfigurationsReactor Configurations

D L

Gas + Solid

Gas + Solid

Up flowDown flow

Riser ReactorRiser Reactor

Upward particle velocity

Sp UUU 0

Superficial gas velocity

Settling velocity of particle

tS UU Terminal velocity of a single particle in an unbounded fluid

Gas + Solids

Note: Concentration of solids is low

Terminal VelocityTerminal Velocity

2/14

Dg

gspt C

gdU

,Re pD fC

Reynolds Number RegionReynolds Number Region

1Re p

1818

22 pgdgdU pgspt

Strokes Region

500Re1 p

3/122

225

4

g

gspt

gdU

For Higher Solid For Higher Solid ConcentrationsConcentrations

17.2

64.011.4

ts

ts

UU

eUU

ExampleExample

If we considered If we considered UU0 0 ~~UUpp, and we have 1 mol of , and we have 1 mol of gas reacting with 1 mol of solid of Mgas reacting with 1 mol of solid of Mwtwt = 100 = 100 g/mol and g/mol and pp = 2 g/cm = 2 g/cm33

1

400

/2100

)(400,22

3

3

cmgg

STPcm

V

V

solids

gas

1

9975.0400

11

For uniform gas compositionFor uniform gas composition Plug flow of solidsPlug flow of solids

iitXs

iipXs

RRUUH

RRUH

01

1

Where, = time for complete reaction

For Strokes Region and For Strokes Region and SCMSCM

With no Mass Transfer (MT) of Product Layer With no Mass Transfer (MT) of Product Layer Diffusion (PLD) Resistance:Diffusion (PLD) Resistance:

fArCk

R

,

30

,1

,

3

,

01

18

41

18

4

Rg

RUCk

H

Ck

Rg

Ck

RUH

fArXs

fArfArXs

Critical PointCritical Point

Rcrit

R

HXs=1

Hmax

HcritGoes through a maximum at some critical R

Find HFind Hcritcrit and R and Rcritcrit

Differentiate HDifferentiate HXs=1Xs=1

03

21

18

41

20

,

30

,1

critfAr

fArXs

Rg

UCkdR

dH

Rg

RUCk

H

2/1

0

2

3

g

URcrit

Find HFind Hcritcrit and R and Rcritcrit

Substitute RSubstitute Rcritcrit into H into HXs=1Xs=1 to get H to get Hcritcrit

2/30

2/1

, 2

3

9

7U

gCkH

fArcrit

Note: To transport largest particles through the system:

)( max0 RUU t

Within the Strokes Within the Strokes RegionRegion

2max0 18

4R

gU

Substitute U0 into Hcrit to get

fArcrit Ck

RgH

,

3max0998.0

fArcrit Ck

RgH

,

3max0998.0

Up flow

NotesNotes

Comparison indicates Comparison indicates RRcritcrit ~ 0.77 ~ 0.77 RRmaxmax

One would do a similar calculation for any One would do a similar calculation for any expression for expression for τ τ and also can use more and also can use more general equation for general equation for CCDD..

Note: for Note: for CCA,fA,f to be constant, e.g. at some to be constant, e.g. at some over reactor height, we need small gas over reactor height, we need small gas conversion (or large molar excess of species conversion (or large molar excess of species A in gas phase).A in gas phase).

fAC ,

Down Flow – Raining BedDown Flow – Raining Bed

Gas + Solid

tp

sp

UUU

UUU

0

0

For some simplified case:

iipXs RRUH 1

At it RUU 0 max0 2 RUUUU tsp

For chemical reaction controlling:

fArXs Ck

RgH

,

3max

1 444.0

fAr

Xs Ck

RgH

,

3max

1 444.0

Down flow

RecallRecall

fArcrit Ck

RgH

,

3max0998.0

fArcrit Ck

RgH

,

3max0998.0

Up flow

fArXs Ck

RgH

,

3max

1 444.0

fAr

Xs Ck

RgH

,

3max

1 444.0

Down flow

Ratio 4.4

0998.0

444.0

upflowH

downflowH

crit

crit 4.4

0998.0

444.0

upflowH

downflowH

crit

crit